Prisons minister Rory Stewart said: “This new framework will give governors the tools to set clear behavioural standards for offenders and the consequences should these not be met.”

The new incentives come after it emerged that serious failings risked allowing prisoners to make contact with victims from jail.

An inspection report on HMP High Down in Banstead, Surrey, said public protection assessments to determine whether mail and phone call monitoring was needed were not routinely completed for new arrivals.

“This meant that some prisoners who presented a risk to people in the community did not have these restrictions applied, enabling them to contact victims or potential victims without the fear of being detected,” the assessment said.

It noted that a list of prisoners to be monitored held by the mail monitoring team was not up to date.

Inspectors who visited the jail in May described how one high-risk prisoner who should have had his letters monitored had been missed over recent weeks, and there was evidence of him regularly contacting a “vulnerable person” in the community.

The report from Chief Inspector of Prisons Peter Clarke said: “Public protection restrictions were not used well enough to prevent prisoners presenting a high risk of harm from contacting their victims.”

High Down, a category B prison in Surrey, held 1,130 men at the time of the inspection.

It is one of around 20 state-run prisons to have introduced in-cell telephones. Plans were announced earlier this year to roll out the technology in a further 20 establishments in England and Wales.

The inspection report on High Down said: “The introduction of in-cell telephones represented important progress.

“However, the shortage of staff in the public protection team resulted in delays for prisoners whose telephone numbers needed to be checked by staff before allowing contact, although staff were working hard to reduce the backlog.”

A Prison Service spokeswoman said: “Prisons are required to have robust monitoring procedures in place for mail and telephone use.

“Immediate action was taken following the inspection in May with additional resources now invested to ensure mail and telephone calls are monitored regularly and properly.”